Computation of stable interval Kalman filter bounds for their use in robust state estimation for an uninhabited surface vehicle with bounded indeterminate system dynamics

This paper implements an interval Kalman filter (IKF) for the navigation of the Springer uninhabited surface vehicle. Interval filters become necessary when the system dynamics are not known precisely or vary unpredictably, but can nevertheless be described in terms of bounded intervals. Such filters based on interval systems require the use of interval arithmetic (IA) for their operation. One of the main limitations to such techniques is that the interval bounds of the computed filter estimates often diverge due to the overly conservative nature of IA. In this paper, ellipsoidal rather than direct IA is used to operate the IKF and obtain bounds of the interval estimates that do not diverge due to the so called wrapping effect. From these bounds, a weighted average is computed at each time-step that is close to the true system state. To obtain this weighting, an artificial neural network (ANN) is previously trained to map residuals of an ordinary Kalman filter to the optimal weights, and this trained network is then used online in new tracking missions.